I spotted a forum thread at My Les Paul which had some nice discussion. I posted my own comments there, and have copied them here as well. Hope you find it useful:
The question is not answered all that easily… A scale or a chord can have a root, and as pointed out by others, the root is not necessarily the lowest note of the chord.
You start to delve into the area of inversions and modes here. An inversion is a chord where the lowest note is not the root. So, G,C,E could be thought of as a C chord, even though the lowest note is not a C. This can be written as C/G, which you’ve probably seen before. There are many inversions of the same chord going up and down the scales and the neck of the guitar, typically achieved by playing your open chord shapes but using bars at different parts of the neck, or simplified chords using less than all 6 strings.
Modes are similar in a way, in that you begin by playing a major scale, but not the “ROOT” note, i.e. play a C major scale, but starting on D (this would be Dorian mode). As each mode has an associated root chord (C ionian, D dorian, E phrygian, F myxolidian, G Lydian, A Aeolian and B locrian) you can write a song in each of these modes by using the chords from C major but changing the root chord, i.e. maybe the chord that you keep coming back to, and the scale that you base your melodies around to be a note (or chord) from C major, other than C.
Off the top of my head, Guns and Roses Sweet Child of Mine is a good example of a song in myxolidian mode. And I think that David Bowie’s “Man Who Sold the World” is a good example of switching between modes from Phygian mode to Aeolian (I think!!!).
Hope this helps, and doesn’t just make it more confusing. I find this quite useful:
The Guitar Master’s Interactive Circle of Fifths
Tags: chord, modes, scale, theory
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